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A Random Boolean Network Model And Deterministic Chaos, Mihaela Teodora Matache, Jack Heidel
A Random Boolean Network Model And Deterministic Chaos, Mihaela Teodora Matache, Jack Heidel
Mathematics Faculty Publications
This paper considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes, which may vary from one node to another. This is an extension of a model studied by Andrecut and Ali ( [5]) who consider the same number of parents for all nodes. We make use of the same Boolean rule as the authors of [5], provide a generalization of the formula for the probability of finding a node in state 1 at a time t and use simulation methods to generate consecutive states of the …
A Fixed Point Theorem For Analytic Functions, Valentin Matache
A Fixed Point Theorem For Analytic Functions, Valentin Matache
Mathematics Faculty Publications
We prove that each analytic self-map of the open unit disk which interpolates between certain n-tuples must have a fixed point.
Palindrome-Polynomials With Roots On The Unit Circle, John Konvalina, Valentin Matache
Palindrome-Polynomials With Roots On The Unit Circle, John Konvalina, Valentin Matache
Mathematics Faculty Publications
Given a polynomial f(x) of degree n, let fr(x) denote its reciprocal, i.e., fr(x) = xnf(1=x). If a polynomial is equal to its reciprocal, we call it a palindrome since the coefficients are the same when read backwards or forwards. In this mathematical note we show that palindromes whose coefficients satisfy a certain magnitude-condition must have a root on the unit circle...